Quasitruncated cuboctahedron

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Quasitruncated cuboctahedron
Rank3
TypeUniform
Notation
Bowers style acronymQuitco
Coxeter diagramx4/3x3x ()
Elements
Faces12 squares, 8 hexagons, 6 octagrams
Edges24+24+24
Vertices48
Vertex figureScalene triangle, edge lengths 2, 3, 2–2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles8/3–4: 135°
 8/3–6:
 6–4:
Central density-1
Number of external pieces146
Level of complexity26
Related polytopes
ArmySemi-uniform Girco, edge lengths (octagons), (ditrigon-rectangle)
RegimentQuitco
DualGreat disdyakis dodecahedron
ConjugateGreat rhombicuboctahedron
Convex coreOctahedron
Abstract & topological properties
Flag count288
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryB3, order 48
Flag orbits6
ConvexNo
NatureTame

The quasitruncated cuboctahedron or quitco, also called the great truncated cuboctahedron, is a uniform polyhedron. It consists of 12 squares, 8 hexagons, and 6 octagrams, with one of each type of face meeting per vertex. It can be obtained by quasicantitruncation of the cube or octahedron, or equivalently by quasitruncating the vertices of a cuboctahedron and then adjusting the edge lengths to be all equal.

Vertex coordinates[edit | edit source]

A quasitruncated cuboctahedron of edge length 1 has vertex coordinates given by all permutations of:

  • .

External links[edit | edit source]